For almost 40 years commercial supersonic flight over land has been prohibited because of the negative impact of sonic booms. During that time, technology advances have raised the possibility of a muted sonic boom—a sonic “puff”—that could be acceptable over populated areas. This paper reviews the physics of sonic boom generation and propagation, and why booms from conventional aircraft are usually N-waves with unacceptably large shock waves. The low-boom shaping technology that can minimize shocks, thus reducing sonic boom loudness to acceptable levels, is presented. The success of the DARPA/NASA Shaped Sonic Boom Demonstrator in validating shaping theory is discussed. Concepts for attaining practical aircraft configurations, versus ideal optimal shapes, are described.